Seismic shear wave splitting, utilizing Multi-Source and Multi-Component (Ms-Mc) shear-wave seismic data, is one technique for the detection of fracture zones and for the extraction of lithologic information in subsurface geologic strata. In patricular, four. component (employing both in-line and cross-line sources and receivers) Ms-Mc shear wave data has been shown to be an effective tool for the detection of fracture zones in subsurface geologic strata. One difficulty, in processing such data, is determining the rotation angle for aligning the shear wave sources and detectors with the shear waves propagating within the earth.
Alford introduced a coordinate transform (often refered to as "Alford Rotation") to rotate four component seismic shear wave data (See Alford, R. M, "Shear Data in the Presence of Azimuthal Anisotropy", Expanded Abstracts, 56th Int'l. SEG Mtg. Houston, pp. 476-479, 1986; and U.S. Pat. Nos.: 4,817,061; 4,803,666; 5,025,332; 4,903,244; and 5,029,146). In general, the process involves choosing a number of rotation angles, applying these angles to the four component data set, and finding an angle by visual comparison which minimized the seismic energy in the mis-matched components.
Although Alford Rotation has been proven to be useful, there are some limitations. Alford Rotation works well when fracture orientations along a seismic line are uniform or sectionally uniform, or when the acquisition direction is not aligned with azimuthal anisotropic direction that is associated with fracturing in a layer with possible hydrocarbon content. However, when shear waves pass through a multi-layer medium, they undergo re-splitting each layer boundary where the anisotropic principle axes change. Thus, deeper subsurface anisotropy is affected by the layers adjacent to the observation point on the surface, Data processing in presence of anisotropy in multi-layer medium is quite complicated; a simple Alford Rotation does not, in general, provide the desired results. More importantly, the output is coordinate-system dependent. The process also assumes a constant rotation angle for all times, or at least for specific time windows. In general, the inhomogeneity and complexity of subsurface geological structures, do not satisfy this condition. In other words, the application of Alford Rotation is limited and, if not correctly applied, could possibly introduce significant numerical errors.
Others have developed methods and processes to gain a better understanding of anisotropy and overcome some earlier problems. Thomsen (See Thomsen, L. A., "Reflection seismology over azimuthal anisotropic media", Geophysics, 53(3), pp. 304-313, 1988) gave a derivation of the basic Alford process and an alternative process (often refered to as "Thomsen Rotation) which employs only one polarization of source (i.e., a single-source/multi-receiver, SS/MR technique; also see U.S. Pat. Nos. 4,888,743 and 4,933,913). Nicoletis (See Nicoletis, L., Client, C., and Lefeuvre, F., "Shear-wave splitting measurement from multi-shot VSP data", Expanded Abstracts, 58th Intl. SEG Mtg., Anaheim, pp. 527-530, 1988); Murtha (See Murtha, P. E., "Estimation of the rotation transformation angle for shear wave data acquired in azimuthally anisotropic regions", AGU/SEG Chapman Conference on Seismic Anisotropy of the Earth's Crust, Berkeley, Calif., 1988); and Li and Crampin (See Li, X. Y. and Crampin, S., "Case studies of complex component analysis of shear-wave splitting", Expanded Abstracts, 60th Intl. SEG Mtg, San Francisco, pp. 1427-1430, 1990; and "Linear-transform techniques for analyzing shear-wave splitting in four-component seismic data", Expanded Abstracts, 61st Intl. SEG Mtg., pp. 51-54, 1991); have made other contributions. Some of these methods have worked well on synthetic data; however, when applied to field data, some methods produced unstable results in the determination of rotation angles.
Clearly, improvement is needed.